Cooperation turns out to be much more likely when we include the interaction between costly punishment and a reputational system into the mix, assigning a better reputation to agents that opt-out from the game than to those that participate but withhold their contribution. It should be noted that the emergence of high levels of cooperation in this setup is surprising as the presence of anti-social punishment has been found to reduce the levels of cooperation ([1]} and replicated in Fig. REF ) in the OPGG. Given that the success of the combination of punishment and reputation in sustaining cooperation is much higher than the success of either of the two alone, the two mechanisms act in synergy with each other. The ecosystem of strategies that thrive in this environment is made up of strategies whose main (or sole) action is cooperation, who for the most part do not employ the punishment device at all, with a smaller but material proportion punishing pro-socially.
For each conditional strategy, there are significant mutual transitions between the non-punishing and the pro-socially punishing variants, indicating a minor but present role for the latter in preserving cooperation. This cooperative environment relies on the regular influx of mutant strategists to mitigate the second-order free-rider problem, moderating the cyclical dynamics it induces. New punishing agents introduced into the population are progressively transformed into the non punishing variants. Their role is confirmed by SM Fig. SREF  where in the presence of both reputation and punishment, cooperation levels decrease for lower mutation rates.
